Use green's theorem to evaluate the line integral. assume the curve is oriented counterclockwise.
contour integral subscript upper c superscript baseline left parenthesis 3 x plus arctangent y squared right parenthesis dy minus left parenthesis 8 y squared plus hyperbolic sine x right parenthesis dx∮ c(3x+arctany2dy−8y2+sinhx)dx,
where c is the boundary of the square with vertices
left parenthesis 1 comma 5 right parenthesis comma(1, 5),
left parenthesis 2 comma 5 right parenthesis comma(2, 5),
left parenthesis 2 comma 6 right parenthesis comma(2, 6),
and left parenthesis 1 comma 6 right parenthesis (1,6)